Question

The sum of the measures of interior angles of a polygon of n sides is equal to

• A. $2n$ right angles
• B. $(2n-2)$ right angles
• C. $2(n-2)$ right angles
• D. $2(n-4)$ right angles

Answer 1

Answer: (C)

$2(n-2)$ right angles

If a polygon has $n$ sides, then it is divided into $(n-2)$ triangles.

• We know that the sum of the angles of triangle = 180${}^{\circ }$.

Therefore, the sum of the angles of $(n-2)$ triangles = 180 $\times$ $(n-2)$

$\Rightarrow$ 2$\times$right angles$\times$$(n-2)$

$\Rightarrow 2(n-2)$ right angles